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Write converse, inverse and contrapositive of the following statement. A family becomes literate if the woman in it is literate. - Mathematics and Statistics

Sum

Write converse, inverse and contrapositive of the following statement.

A family becomes literate if the woman in it is literate.

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Solution

Let p: The woman in the family is literate.
      q: A family becomes literate.
Then the symbolic form of the given statement is p → q.
Converse: q → p is the converse of p → q.
i.e. If a family becomes literate, then the woman in it is literate.
Inverse: ∼ p → ∼ q is the inverse of p → q.
i.e. If the woman in the family is not literate, then the family does not become literate.
Contrapositive: ∼ q → ∼ p is the contrapositive of p → q.
i.e. If a family does not become literate, then the woman in it is not literate.

Concept: Converse, Inverse, and Contrapositive
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